Revisiting Nonlinear In-Plane Elastic Buckling and Postbuckling Analysis of Shallow Circular Arches under a Central Concentrated Load

This paper revisits the nonlinear in-plane analysis of a shallow pin-ended circular arch under a central concentrated load. It is found that the arch may have multiple equilibrium branches and limit points, and a modified slenderness of the arch defined in the paper plays an important role in the number of the limit points and equilibrium branches. The analytical solution for the specific modified slendernesses that switch the number of equilibrium branches and limit points is derived. The analytical solutions for the load, axial force, and radial displacements corresponding to the specific modified slendernesses are also derived. This paper deepens the understanding for the geometric nonlinear analysis of circular arches and their geometric softening and stiffening behavior and provides useful benchmarks for the analyses of shallow arches. In addition, this paper extends the current solutions of nonlinear equilibrium of arches associated with axial compression to those associated with axial tension caused by large deformations.